Difference between revisions of "Mustafa Altun"
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=== Self-Duality === | === Self-Duality === | ||
The problem of testing whether a monotone Boolean function in irredundant disjuntive normal form (IDNF) is self-dual is one of few problems in circuit complexity whose precise tractability status is unknown. We have focused on this famous problem. We have shown that monotone self-dual Boolean functions in IDNF do not have more variables than disjuncts. We have | The problem of testing whether a monotone Boolean function in irredundant disjuntive normal form (IDNF) is self-dual is one of few problems in circuit complexity whose precise tractability status is unknown. We have focused on this famous problem. We have shown that monotone self-dual Boolean functions in IDNF do not have more variables than disjuncts. We have proposed an algorithm to test whether a self-dual Boolean function in IDNF with ''n'' variables and ''n'' disjuncts is self-dual. The algorithm runs in <math>O(n^4)</math> time. | ||
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Revision as of 14:36, 10 February 2012
I am a Ph.D. candidate in the Dept. of Electrical and Computer Engineering at the University of Minnesota, Twin Cities Campus.
Current Research
I am pursuing research in the area of logic synthesis for emerging technologies. I also have a particular interest in combinatorics, more specifically hypergraphs.
Self-Duality
The problem of testing whether a monotone Boolean function in irredundant disjuntive normal form (IDNF) is self-dual is one of few problems in circuit complexity whose precise tractability status is unknown. We have focused on this famous problem. We have shown that monotone self-dual Boolean functions in IDNF do not have more variables than disjuncts. We have proposed an algorithm to test whether a self-dual Boolean function in IDNF with n variables and n disjuncts is self-dual. The algorithm runs in
time.
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Switching Lattices
In his seminal Master's Thesis, Claude Shannon made the connection between Boolean algebra and switching circuits. He considered two-terminal switches corresponding to electromagnetic relays. A Boolean function can be implemented in terms of connectivity across a network of switches, often arranged in a series/parallel configuration. We have developed a method for synthesizing Boolean functions with networks of four-terminal switches. Our model is applicable for variety of nanoscale technologies, such as nanowire crossbar arrays, as molecular switch-based structures.
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Percolation for Robust Computation
We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of percolation. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. This phenomenon is exploited to compute Boolean functions robustly, in the presence of defects.
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Contact Information
- Email Address: altu0006@umn.edu
- Cell Phone: 612-978-2955
- Address: 200 Union St. S.E., Room 4-136, Minneapolis, MN 55455